Investigations Blog

Reflections on NCSM/NCTM, Part 2

Six of our staff traveled to San Diego to attend the NCSM and NCTM conferences at the beginning of April. Below are four staff members’ reflections on a session that stood out to them. (Read the first three here.) Keith: “The Iris Carl Equity Address: Equity and Agency from Inside the Classroom” by José Luis Vilson (NCTM) José Vilson began his talk with an elegant, powerful statement — “Equity is belonging.” — and then challenged us with this question: “Do you believe your students belong?”...

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Reflections on NCSM/NCTM, Part 1

Six of our staff traveled to San Diego to attend the NCSM and NCTM conferences at the beginning of April. Below are three staff members’ reflections on a session that stood out to them. Four more to follow next time. Keith: “From Oakland to Wakanda: Transforming Mathematics Classrooms to Become Empowering Spaces” by Imani Masters Goffney (NCTM) Imani Masters Goffney gave a fascinating talk about making math classrooms equitable spaces for learning. She used the movie Black Panther as a context...

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A Conversation about “Key Words”

In my years of leading in-person and online professional development, the idea of teaching students that certain “key words” signify a particular operation (e.g. “altogether means add”) often comes up when discussing story problems. People also generally see the power of the story problem routine that Investigations uses to support students in making sense of and solving story problems. This led me to start a conversation in a recent online course about the juxtaposition between the focus of...

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A Grade 5 Q&A: Percents

Question: Why was the work with percents taken out of the 5th grade curriculum in the 3rd edition? Answer: In the 1st and 2nd editions of Investigations, there was a unit (Name that Portion and What’s That Portion?) that included lessons that connected what 5th graders already knew about percents to what they already knew about fractions and decimals. These concepts were taught together, rather than separately, and built strong conceptual understandings of the meaning of percents and their...

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Helping with Math Homework

In schools that use Investigations, families often feel unsure of how to help their children with math homework. Many parents/caregivers have told me that they don’t understand the strategies their children are using and don’t know what to do if their child is struggling with a homework assignment. The math education field has work to do to help families make sense of how math is being taught, and to help them figure out how to support their children in mathematics learning. However, I think a...

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Multiplication in 5th Grade: What Are Some Issues?

Last year, my colleague Keith and I worked a few times with a group of 5th grade teachers. One of the questions they asked us to help them think about related to this 5th grade benchmark: “Fluently solve multidigit multiplication problems using a variety of strategies including the U.S. standard algorithm.” They told us that they had students who could multiply 2-digits by 2-digits successfully but struggled with 3-digit by 2-digit multiplication problems. They wanted to discuss the...

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A Grade 2 Q&A: The Size of the Numbers

Question: If the CCSS indicates that Grade 2 students are supposed to be working with numbers to 1,000, why doesn’t this work begin sooner? Why are students still working with numbers under 20 and numbers under 100 for so much of the year? Answer: The Common Core State Standards at Grade 2 include work with numbers up to 1,000, but it is important to look closely at what students are expected to do with these numbers. In Grade 2 students are developing efficient and accurate strategies...

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Q&A: The Order of the Units

Question: Can the Investigations units be taught in a different order than suggested?Answer: The first edition of Investigations was written as a “replacement unit” model where individual units within a grade were somewhat less dependent on previous units, and schools and districts often chose their own sequence, or decided to teach only 3 or 4 units the first year of implementation. That was the 1990s! The units in the 2nd and 3rd editions were written as a complete, coherent, full-year...

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The Bad Rep of Word Problems: “Two trains leave the station…”

When people want to make a joke about how difficult, convoluted, or inaccessible word problems are, they often cite some version of the “two trains” problem. You can see an example of this problem here: Maybe you want to try solving this problem yourself before reading on. (Maybe not!) The “two trains” problem has become an emblem in popular culture. Saying the opening phrase, “Two trains leave different stations at the same time …,” invariably results in uncomfortable laughter. It surfaces...

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Q&A: Mathematical Vocabulary in Investigations 3

Question: How does Investigations approach the teaching and learning of mathematical vocabulary?Answer: In Investigations 3, mathematical vocabulary is introduced as a natural part of the conversation during activities and discussions, along-side students’ own words. Rather than memorizing the definitions of new terms, students come to understand such words as factor or area or symmetry as they investigate and discuss new concepts. Hearing new mathematical terms used regularly, and having...

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